{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 卡方分布（Chi-Squared Distribution）\n",
    "***\n",
    "## 定义\n",
    "\n",
    "若n个相互独立的随机变量\\xi^1，ξ2，…，ξn服从标准正态分布，则这n个服从标准正态分布的随机变量的平方和Q=\\sum_{i=1}^{n}\\xi_i^2构成一个新的随机变量，该随机变量的分布规律称为Χ2卡方分布(Chi-Square Distribution)。卡方分布的参数是u自由度，记作Q~Χ2(u)或者Q~X_u^2。其中u=n-k，k为限制条件数。卡方分布是由正态分布构造而成的一个新的分布，当自由度u很大时，Χ2分布近似为正态分布。\n",
    "\n",
    "卡方检验的基本思想是根据样本数据推断总体的频次与期望频次是否有显著性差异\n",
    "\n",
    "## 公式\n",
    "\n",
    "$$\n",
    " \\begin{equation}\n",
    "    f(x|k) =\n",
    "    \\begin{cases}\n",
    "      \\frac{x^{\\frac{k}{2}-1}e^{-\\frac{x}{2}}}{2^{\\frac{k}{2}}\\Gamma(\\frac{k}{2})}, & \\text{if}\\ x>0 \\\\\n",
    "      0, & \\text{otherwise}\n",
    "    \\end{cases}\n",
    "  \\end{equation}\n",
    "$$<br>\n",
    "where\n",
    "$$ \\Gamma(n) = (n-1)! $$<br>\n",
    "and $k$ denotes the degrees of freedom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(15,8))\n",
    "datas = np.linspace(0, 20, 100)\n",
    "# PDF\n",
    "plt.fill_between(datas,stats.chi2.pdf(datas, df=5),hatch=\"/\")\n",
    "\n",
    "plt.fill_between(datas,stats.chi2.pdf(datas, df=8),hatch=\"*\")\n",
    "plt.fill_between(datas,stats.chi2.pdf(datas, df=10),hatch=\"+\")\n",
    "\n",
    "plt.fill_between(datas,stats.chi2.pdf(datas, df=15),hatch=\"//\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
